Phonon spectra, electronic, and thermodynamic properties of WS₂ nanotubes

Abstract

Hybrid density functional theory calculations are performed for the first time on the phonon dispersion and thermodynamic properties of WS -based single-wall nanotubes. Symmetry analysis is presented for phonon modes in nanotubes using the standard (crystallographic) factorization for line groups. Symmetry and the number of infra-red and Raman active modes in achiral WS nanotubes are given for armchair and zigzag chiralities. It is demonstrated that a number of infrared and Raman active modes is independent on the nanotube diameter. The zone-folding approach is applied to find out an impact of curvature on electron and phonon band structure of nanotubes rolled up from the monolayer. Phonon frequencies obtained both for layers and nanotubes are used to compute the thermal contributions to their thermodynamic functions. The temperature dependences of energy, entropy, and heat capacity of nanotubes are estimated with respect to those of the monolayer. The role of phonons in the stability estimation of nanotubes is discussed based on Helmholtz free energy calculations. © 2017 Wiley Periodicals, Inc.

First‐Principles Calculations of Phonons and Thermodynamic Properties of Zr(Hf)S2‐Based Nanotubes

“…Because of this, the hybrid density functionals are preferable over LDA or GGA for the narrow gap semiconductors due to the possibility of producing by them the wrong metallic state of semiconductor. [37,38] This functional reproduces the experimental electron band gap of bulk MeS 2 crystals with good accuracy. The HSE06 hybrid exchangecorrelation functional [36] was adopted in this work for the reason of the compatibility with our recent results for phonon and thermodynamic properties of MoS 2 and WS 2 nanotubes.…”

“…Figure 8 shows the temperature dependence of the Helmholtz free energy difference between the monolayer and small diameter nanotubes. [37] The results obtained demonstrate the small contribution of the phonons to NTs relative stability. The slope of plots in Figure 8 is positive, thus the temperature-dependent contribution slightly reduces the nanotube stability of the narrow nanotubes at elevated temperatures.…”

“…[37,38] It was found that the temperature dependence of the heat capacity of ZrS 2 and HfS 2 monolayers is very similar.…”

“…The self-consistent solution of one-electron equations was iterated within a threshold of 3 × 10 −7 kJ mol −1 (in geometry optimization) and 3 × 10 −8 kJ mol −1 (in phonon calculations). [37,38,42] The parameters for the modified DC are given in Table S2 of Supporting Information. [37,38,42] The parameters for the modified DC are given in Table S2 of Supporting Information.…”

“…The values obtained in this work are given in Table S4. [37,56] There is no appreciable difference between strain energy of ac and zz nanotubes. Figure 5 shows the strain energy dependence on average diameter D for ZrS 2 and HfS 2 nanotubes.…”